scholarly journals From deep TLS validation to ensembles of atomic models built from elemental motions

2015 ◽  
Author(s):  
Alexandre Urzhumtsev ◽  
Pavel Afonine ◽  
Andrew H Van Benschoten ◽  
James Fraser ◽  
Paul D Adams
Keyword(s):  
Rigid Body ◽  
Diffraction Data ◽  
Harmonic Vibration ◽  
Mathematical Framework ◽  
Matrix Elements ◽  
Computational Tools ◽  
X Ray ◽  
Structural Ensembles ◽  
The Matrix ◽  
Rigid Body Motions

The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three matrices (T, L and S) describe harmonic vibration, libration and their correlation. Because these matrices describe specific motions, they impose a number of conditions on their elements. Ignoring these conditions while refining the matrix elements may result in matrices that cannot be interpreted in terms of physically realistic motions. We describe a mathematical framework and the computational tools to analyze refined TLS matrices through their decomposition into descriptors of underlying motions. This allows for straightforward validation and identification of implausible TLS parameters. An algorithm for the generation of structural ensembles that are consistent with given TLS parameters, implemented as a part of the Phenix project, is also described.

scholarly journals Liquid-like and rigid-body motions in molecular-dynamics simulations of a crystalline protein

2019 ◽  
Author(s):  
David C. Wych ◽  
James S. Fraser ◽  
David L. Mobley ◽  
Michael E. Wall
Keyword(s):  
Molecular Dynamics ◽  
Rigid Body ◽  
Diffraction Data ◽  
Md Simulations ◽  
X Ray Diffraction ◽  
X Ray ◽  
Atom Pairs ◽  
Collective Motions ◽  
Rigid Body Motions ◽  
Insight Into

AbstractTo gain insight into crystalline protein dynamics, we performed molecular-dynamics (MD) simulations of a periodic 2×2×2 supercell of staphylococcal nuclease. We used the resulting MD trajectories to simulate X-ray diffraction and to study collective motions. The agreement of simulated X-ray diffraction with the data is comparable to previous MD simulation studies. We studied collective motions by analyzing statistically the covariance of alpha-carbon position displacements. The covariance decreases exponentially with the distance between atoms, which is consistent with a liquid-like motions (LLM) model, in which the protein behaves like a soft material. To gain finer insight into the collective motions, we examined the covariance behavior within a protein molecule (intra-protein) and between different protein molecules (inter-protein). The inter-protein atom pairs, which dominate the overall statistics, exhibit LLM behavior; however, the intra-protein pairs exhibit behavior that is consistent with a superposition of LLM and rigid-body motions (RBM). Our results indicate that LLM behavior of global dynamics is present in MD simulations of a protein crystal. They also show that RBM behavior is detectable in the simulations but that it is subsumed by the LLM behavior. Finally the results provide clues about how correlated motions of atom pairs both within and across proteins might manifest in diffraction data. Overall our findings increase our understanding of the connection between molecular motions and diffraction data, and therefore advance efforts to extract information about functionally important motions from crystallography experiments.

scholarly journals Characterization of FeOOH Nanoparticles and Amorphous Silica Matrix in an FeOOH-SiO2Nanocomposite

2008 ◽  
Vol 2008 ◽  
pp. 1-6 ◽  
Author(s):  
Guido Ennas ◽  
Maria F. Casula ◽  
Sergio Marras ◽  
Gabriele Navarra ◽  
Alessandra Scano ◽  
...  
Keyword(s):  
Hydrochloric Acid ◽  
Amorphous Silica ◽  
Diffraction Data ◽  
Silica Matrix ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Matrix ◽  
Curve Method ◽  
Hydrolysis Of

A nanocomposite with an FeOOH/SiO2ratio equal to 17.7 wt% and the pertinent matrix, obtained by etching away the nanoparticles through reaction with hydrochloric acid, were investigated by XRD, TGA-DTA, heliostereopicnometry, BET, and TEM techniques. The study shows the presence in the nanocomposite of ferrihydrite nanoparticles phase with average dimensions around 4 nm. The FeOOH nanoparticles structure was analyzed by synchrotron X-ray diffraction data using the distribution difference curve method. The porous structure of the matrix resulting by etching away the nanoparticles differs significantly from that of a pureSiO2sample obtained by hydrolysis of TEOS under the same operative conditions followed in the nanocomposite preparation.

Kinematics Meets Crystallography: The Concept of a Motion Space

2014 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Rigid Body ◽  
Molecular Structures ◽  
New Drugs ◽  
Dimensional Structure ◽  
Biological Macromolecules ◽  
Molecular Replacement ◽  
X Ray Diffraction ◽  
X Ray ◽  
Rigid Body Motions ◽  
Diffraction Patterns

In this paper, it is shown how rigid-body kinematics can be used to assist in determining the atomic structure of proteins and nucleic acids when using x-ray crystallography, which is a powerful method for structure determination. The importance of determining molecular structures for understanding biological processes and for the design of new drugs is well known. Phasing is a necessary step in determining the three-dimensional structure of molecules from x-ray diffraction patterns. A computational approach called molecular replacement (MR) is a well-established method for phasing of x-ray diffraction patterns for crystals composed of biological macromolecules. In MR, a search is performed over positions and orientations of a known biomolecular structure within a model of the crystallographic asymmetric unit, or, equivalently, multiple symmetry-related molecules in the crystallographic unit cell. Unlike the discrete space groups known to crystallographers and the continuous rigid-body motions known to kinematicians, the set of motions over which molecular replacement searches are performed does not form a group. Rather, it is a coset space of the group of continuous rigid-body motions, SE(3), with respect to the crystallographic space group of the crystal, which is a discrete sub-group of SE(3). Properties of these ‘motion spaces’ (which are compact manifolds) are investigated here.

scholarly journals From deep TLS validation to ensembles of atomic models built from elemental motions

2015 ◽  
Vol 71 (8) ◽  
pp. 1668-1683 ◽  
Author(s):  
Alexandre Urzhumtsev ◽  
Pavel V. Afonine ◽  
Andrew H. Van Benschoten ◽  
James S. Fraser ◽  
Paul D. Adams
Keyword(s):  
Molecular Mechanisms ◽  
Mathematical Framework ◽  
Matrix Elements ◽  
Correlated Motions ◽  
Molecular Movement ◽  
Atomic Vibrations ◽  
The Matrix ◽  
Independent Parameters ◽  
Structural Ensemble ◽  
Shed Light

The translation–libration–screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because theT,LandSmatrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy several conditions. Refining theT,LandSmatrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of thePHENIXproject.

Kinematics Meets Crystallography: The Concept of a Motion Space1

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Rigid Body ◽  
Discrete Subgroup ◽  
Molecular Structures ◽  
New Drugs ◽  
Dimensional Structure ◽  
Biological Macromolecules ◽  
X Ray Diffraction ◽  
X Ray ◽  
Rigid Body Motions ◽  
Diffraction Patterns

In this paper, it is shown how rigid-body kinematics can be used to assist in determining the atomic structure of proteins and nucleic acids when using x-ray crystallography, which is a powerful method for structure determination. The importance of determining molecular structures for understanding biological processes and for the design of new drugs is well known. Phasing is a necessary step in determining the three-dimensional structure of molecules from x-ray diffraction patterns. A computational approach called molecular replacement (MR) is a well-established method for phasing of x-ray diffraction patterns for crystals composed of biological macromolecules. In MR, a search is performed over positions and orientations of a known biomolecular structure within a model of the crystallographic asymmetric unit, or, equivalently, multiple symmetry-related molecules in the crystallographic unit cell. Unlike the discrete space groups known to crystallographers and the continuous rigid-body motions known to kinematicians, the set of motions over which MR searches are performed does not form a group. Rather, it is a coset space of the group of continuous rigid-body motions, SE(3), with respect to the crystallographic space group of the crystal, which is a discrete subgroup of SE(3). Properties of these “motion spaces” (which are compact manifolds) are investigated here.

scholarly journals Vectorial parameterizations of pose

Robotica ◽  
2021 ◽  
pp. 1-19
Author(s):  
Timothy D. Barfoot ◽  
James R. Forbes ◽  
Gabriele M. T. D’Eleuterio
Keyword(s):  
Computer Vision ◽  
Rigid Body ◽  
Pose Estimation ◽  
Lie Group ◽  
Matrix Exponential ◽  
Uncertainty Representation ◽  
The Matrix ◽  
Alignment Problem ◽  
Cayley Transformation ◽  
Rigid Body Motions

Abstract Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation – together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the $4 \times 4$ representation common in robotics and also demonstrate three different examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem, our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.

Crystal structure and diffraction data for a polymorph of voglibose (C10H21NO7)

2010 ◽  
Vol 25 (S1) ◽  
pp. S28-S30
Author(s):  
G. Q. Zhang ◽  
G. L. Lv
Keyword(s):  
Crystal Structure ◽  
Simulated Annealing ◽  
Rigid Body ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Molecular Structures ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Crystal And Molecular Structures

X-ray powder diffraction data of voglibose are reported, and its crystal and molecular structures were determined by simulated annealing and rigid-body Rietveld refinement methods. Voglibose was found to be crystallized in triclinic symmetry with space group P-1. The lattice parameters were determined to be a=6.1974(6) Å, b=6.9918(5) Å, c=7.3955(9) Å, α=70.8628(3), β=103.5312(4), γ=94.3867(5)°, V=294.2(2) Å3, and ρcal=1.495 g/cm3. The crystal structure contains isolated C10H21NO7 molecular.

Toward an alignment of the actin molecule within the actin filament

1983 ◽  
Vol 41 ◽  
pp. 450-451
Author(s):  
P.R. Smith ◽  
W.E. Fowler ◽  
U. Aebi
Keyword(s):  
Actin Filament ◽  
Diffraction Data ◽  
Quantitative Estimate ◽  
Molecular Model ◽  
Quantitative Comparison ◽  
Regulatory Proteins ◽  
Essential Information ◽  
X Ray ◽  
Maximum Resolution ◽  
Lack Of Information

An understanding of the specific interactions of actin with regulatory proteins has been limited by the lack of information about the structure of the actin filament. Molecular actin has been studied in actin-DNase I complexes by single crystal X-ray analysis, to a resolution of about 0.6nm, and in the electron microscope where two dimensional actin sheets have been reconstructed to a maximum resolution of 1.5nm. While these studies have shown something of the structure of individual actin molecules, essential information about the orientation of actin in the filament is still unavailable.The work of Egelman & DeRosier has, however, suggested a method which could be used to provide an initial quantitative estimate of the orientation of actin within the filament. This method involves the quantitative comparison of computed diffraction data from single actin filaments with diffraction data derived from synthetic filaments constructed using the molecular model of actin as a building block. Their preliminary work was conducted using a model consisting of two juxtaposed spheres of equal size.

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